Question

The distance between two objects is 10m, the two objects attract each other as 20N. If the mass of the 1st object is 2kg, what is the mass of the 2nd object?

A)1.499×10¹³

B) 1.499×10¹²

C)1.62×10¹³

D)1.3×10¹³
give explanation
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Answer 1

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• Distance between two object is 10m

• F = 20N

• mass of 1st object is 2kg

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Mass of 2nd object

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$\\ \bigstar \boxed{ \bf \: F = \frac{G m_{1} m_{2} }{ {r}^{2} }}$

Here ,

• F Force of attraction

• G Gravitational constant ( 6.67 × 10-¹¹ ) Nm²/kg²

• m(1) is mass of first object

• m(2) is mass of second object

• r is distance between two objects.

Putting values ,

$\\ \sf \: 20 = \frac{6.67 \times {10}^{ - 11} \times 2 \times m_{2} }{ {10}^{2} } \\ \\ \\ \sf \: 20 = {13.34 \times {10}^{ - 11 - 2} \times m_{2}}{} \\ \\ \\ \sf \: 20 = 13 . 34 \times {10}^{ - 13} \times m_{2} \\ \\ \\ \sf \: m_{2} = \frac{20}{13.34 \times {10}^{ - 13} } \\ \\ \\ \boxed{\sf \: \pink{m_{2} = 1.49 \times {10}^{13} kg}}$

Hence , mass of second object is 1.49 × 10¹³ kg.

Option (1) is correct.

Answer 2

Distance between two objects = 10 m

Gravitational Force = 20 N

Mass of first object = 2 kg

Mass of second object = (M) kg {Assume}

We know,

F = GMm/d²

⇒M = Fd²/Gm

⇒M = [(20 N)(10 m)²] ÷ [(6.7 × 10^-11 N m²/kg²) × 2 kg]

⇒M = (20 × 100)/(13.4 × 10^-11) kg

⇒M = 0.149 × 10^14 kg

⇒M = 1.49 × 10^13 kg (A)